The triangle and the open triangle

Gady Kozma

Annales de l'I.H.P. Probabilités et statistiques (2011)

  • Volume: 47, Issue: 1, page 75-79
  • ISSN: 0246-0203

Abstract

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We show that for percolation on any transitive graph, the triangle condition implies the open triangle condition.

How to cite

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Kozma, Gady. "The triangle and the open triangle." Annales de l'I.H.P. Probabilités et statistiques 47.1 (2011): 75-79. <http://eudml.org/doc/242716>.

@article{Kozma2011,
abstract = {We show that for percolation on any transitive graph, the triangle condition implies the open triangle condition.},
author = {Kozma, Gady},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {percolation; Cayley graph; mean-field; triangle condition; operator theory; spectral theory},
language = {eng},
number = {1},
pages = {75-79},
publisher = {Gauthier-Villars},
title = {The triangle and the open triangle},
url = {http://eudml.org/doc/242716},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Kozma, Gady
TI - The triangle and the open triangle
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2011
PB - Gauthier-Villars
VL - 47
IS - 1
SP - 75
EP - 79
AB - We show that for percolation on any transitive graph, the triangle condition implies the open triangle condition.
LA - eng
KW - percolation; Cayley graph; mean-field; triangle condition; operator theory; spectral theory
UR - http://eudml.org/doc/242716
ER -

References

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  10. [10] G. Kozma. Percolation on a product of two trees. In preparation. Zbl1243.60078
  11. [11] G. Kozma and A. Nachmias. The Alexander–Orbach conjecture holds in high dimensions. Invent. Math. 178 (2009) 635–654. Zbl1180.82094
  12. [12] B. G. Nguyen. Gap exponents for percolation processes with triangle condition. J. Statist. Phys. 49 (1987) 235–243. Zbl0962.82521MR923855
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  14. [14] R. H. Schonmann. Mean-field criticality for percolation on planar non-amenable graphs. Comm. Math. Phys. 225 (2002) 453–463. Zbl0990.82027MR1888869

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